TY - JOUR
T1 - Prime divisors in Beatty sequences
AU - Banks, William D.
AU - Shparlinski, Igor E.
PY - 2007/4
Y1 - 2007/4
N2 - We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence ⌊ α n + β ⌋, n = 1, 2, ..., where α, β ∈ R, and α > 0 is irrational. For example, we show thatunder(∑, n ≤ N) ω (⌊ α n + β ⌋) ∼ N log log N and under(∑, n ≤ N) (- 1)Ω (⌊ α n + β ⌋) = o (N), where Ω (k) and ω (k) denote the number of prime divisors of an integer k ≠ 0 counted with and without multiplicities, respectively.
AB - We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence ⌊ α n + β ⌋, n = 1, 2, ..., where α, β ∈ R, and α > 0 is irrational. For example, we show thatunder(∑, n ≤ N) ω (⌊ α n + β ⌋) ∼ N log log N and under(∑, n ≤ N) (- 1)Ω (⌊ α n + β ⌋) = o (N), where Ω (k) and ω (k) denote the number of prime divisors of an integer k ≠ 0 counted with and without multiplicities, respectively.
UR - http://www.scopus.com/inward/record.url?scp=33846867490&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2006.07.011
DO - 10.1016/j.jnt.2006.07.011
M3 - Article
AN - SCOPUS:33846867490
SN - 0022-314X
VL - 123
SP - 413
EP - 425
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -